The gas characteristics of an air vessel is one of the key parameters that determines the protective effect on water hammer pressure. Because of the limitation of the ideal gas state equation applied for a small-volume vessel, the Van der Waals (VDW) equation and Redlich–Kwong (R–K) equation are proposed to numerically simulate the pressure oscillation. The R–K polytropic equation is derived under the assumption that the volume occupied by the air molecules themselves could be ignored. The effects of cohesion pressure under real gas equations are analyzed by using the method of characteristics under different vessel diameters. The results show that cohesion pressure has a significant effect on the small volume vessel. During the first phase of the transient period, the minimum pressure and water depth calculated by a real gas model are obviously lower than that calculated by an ideal gas model. Because VDW cohesion pressure has a stronger influence on the air vessel pressure compared to R–K air cohesion pressure, the amplitude of head oscillation in the vessel calculated by the R–K equation becomes larger. The numerical results of real gas equations can provide a higher safe-depth margin of the water depth required in the small-volume vessel, resulting in the safe operation of the practical pumping pipeline system.
Hydroelectric energy is an increasingly vital and effective renewable energy for modern society. The protective effect on the water hammer in the pipeline, the operational stability of the hydropower system, and the flow regime in the air-cushion surge chamber (ACSC) are three main problems during the design of the hydropower station with an ACSC. Comprehensively comparing the above issues between the horizontal and vertical ACSCs is meaningful. This study established the one-dimensional (1D) model based on the Method of Characteristics (MOC) under large load disturbances (LLD) and the rigid water column theory under small load disturbances (SLD). At the same time, the three-dimensional (3D) model was built based on the Volume of Fluid (VOF) to obtain a more detailed flow regime in the ACSC under the load acceptance condition. The results showed that the vertical ACSC was superior to the horizontal one for its large safe water depth, smaller maximum air pressure, and more stable flow under LLD. In contrast, the horizontal one was better than the vertical one for its extensive water area to calm the SLD during the transient process and smaller fluctuation of the surge under SLD. This study will provide a reference for a future project on selecting the structure of the ACSC.
In the long-distance and high-drop gravitational water supply systems, the water level difference between the upstream and downstream is large. Thus, it is necessary to ensure energy dissipation and pressure head reduction to reduce the pipeline pressure head. The energy dissipation box is a new type of energy dissipation and pressure head reduction device, which is widely used in the gravitational flow transition systems. At present, there is still a dearth of systematic knowledge about the performance of energy dissipation boxes. In this paper, a relationship between the location of the energy dissipation box and the pressure head amplitude is established, a theoretical optimal location equation of the energy dissipation box is derived, and numerical simulations using an engineering example are carried out for verification. The protective effects of an energy dissipation box placed at the theoretical optimal location and an upstream location are compared. The results indicate that for the same valve action time, the optimal position allows effectively reducing the total volume of energy dissipation box. The oscillation amplitudes of the water level in the box and the pressure head behind the box are markedly reduced. Under the condition that the water level oscillation of the energy dissipation box is almost the same, the optimal location offers better pressure head reduction protection performance than the upstream location.
A surge chamber is a common pressure reduction facility in a hydropower plant. Owing to large flow inertia in the upstream headrace tunnel and downstream tailrace tunnel, a hydropower plant with upstream and downstream surge chambers (HPUDSC) was adopted. This paper aimed to investigate the operational stability and nonlinear dynamic behavior of a HPUDSC. Firstly, a nonlinear dynamic model of the HPUDSC system was built. Subsequently, the operational stability and nonlinear dynamic behavior of the HPUDSC system were studied based on Hopf bifurcation theory and numerical simulation. Finally, the influencing factors of stability of the HPUDSC system were investigated. The results indicated the nonlinear HPUDSC system occurred at subcritical Hopf bifurcation, and the stability domain was located above the bifurcation curve, which provided a basis for the tuning of the governor parameters during operation. The dominant factors of stability and dynamic behavior of the HPUDSC system were flow inertia and head loss of the headrace tunnel and the area of the upstream surge chamber. Either increasing the head loss of the headrace tunnel and area of the upstream surge chamber or decreasing the flow inertia of the headrace tunnel could improve the operational stability of the HPUDSC. The proposed conclusions are of crucial engineering value for the stable operation of a HPUDSC.
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